What's the purpose of the Infinity property? - javascript

I accidentally faced an Infinity property in JavaScript and wondered where in the world it can be used? Any real life example please.

You can use it if you don't know what the minimum value of an array or also a mathematical-function is like this:
var minimum = Infinity;
var i = 0;
for(i = 0; i < array.length; i++) {
if(array[i] < minimum) {
// new minimum found
minimum = array[i];
}
}
alert("Minimum: " + minimum);

Here is another real life example:
var x = +prompt('Enter x:'),
y = +prompt('Enter y:'),
value = Math.pow(x, y);
if (value === Infinity || value === -Infinity) {
console.log('The value is too large!');
}
As an example, if the entered values are 1e100 and 100, the power method returns Infinity.

I'm assuming you're asking about why there's an Infinity global property, not why there's a concept of having infinities in the first place, which is another matter.
It allows easy comparison with the Infinity value itself, where you get it from some arithmetic:
function inv(x) {
return x * 100000000000;
}
inv(1e999) === Infinity;
This is especially useful as 1 / 0 is not equal to Infinity in mathematics, so it's not obvious that you can use 1 / 0.
If you want a numeric comparison to always return true, and you're using a variable, you can set the variable to Infinity to always force the condition to be true. Take this example:
var a = Infinity; // some number from elsewhere
var arr = [];
function foo(maxLen) {
if (arr.length < maxLen) arr.push(1);
}
foo(a); // you can't change the function
This could be useful in cases where you can't change the comparison statement used.

Related

A simple for loop questions about -1 and i--

I have what I think surely is a really simple question for most of you. But I have some trouble to get my head around this for loop. What does the -1 in argument.length -1 stand for? Is it the last item? And the i-- that is for decrease by 1?
var plus = function() {
var sum = 0;
for (var i = arguments.length - 1; i >= 0; i--) {
sum += arguments[i];
}
return sum;
}
console.log(plus(2,2,3,657,5643,4465,2,45,6));
When you call arguments.length It will return you the number of elements with the last one accessed with arguments[arguments.length-1] because counting starts with 0.
(the First element is accessed like this arguments[0]).
Here is good documentation for Java but it is the same for JavaScript: https://docs.oracle.com/javase/tutorial/java/nutsandbolts/arrays.html
And yes i-- decreases i for 1. It is different i-- and --i.
Using ++/-- After the Operand
When you use the increment/decrement operator after the operand, the value will be returned before the operand is increased/decreased.
Check out this example:
// Increment
let a = 1;
console.log(a++); // 1
console.log(a); // 2
// Decrement
let b = 1;
console.log(b--); // 1
console.log(b); // 0
When we first log out the value of a, or b, neither has changed. That’s because the original value of the operand is being returned prior to the operand being changed. The next time the operator is used, we get the result of the +1, or -1.
Using ++/-- Before the Operand
If you’d rather make the variable increment/decrement before returning, you simply have to use the increment/decrement operator before the operand:
// Increment
let a = 1;
console.log(++a); // 2
console.log(a); // 2
// Decrement
let b = 1;
console.log(--b); // 0
console.log(b); // 0
As you can see in the above example, but using ++ or -- prior to our variable, the operation executes and adds/subtracts 1 prior to returning. This allows us to instantly log out and see the resulting value.
The - 1 means to subtract 1 from arguments.length. i-- means to decrease i by 1.
You need to know two things here:
arguments is a object type so it has key-value pair of values you passed as a argument into a function. Furthermore, the arguments object is not an Array. It is similar to an Array, but does not have any Array properties except length.
The key of arguments always starts with 0 and ends with one value less than the length of arguments. See the example below the key ends at 8 so you do arguments.length - 1 so that you get 8 instead of 9.
And since you are looping considering the last value first in arguments you do --i.
var plus = function() {
console.log(arguments);
console.log(typeof arguments);
var sum = 0;
for (var i = arguments.length - 1; i >= 0; i--) {
sum += arguments[i];
}
return sum;
}
console.log(plus(2, 2, 3, 657, 5643, 4465, 2, 45, 6));
Alternatively, you can also do i++ as,
var plus = function() {
var sum = 0;
for (var i = 0; i <arguments.length; i++) {
sum += arguments[i];
}
return sum;
}
console.log(plus(2, 2, 3, 657, 5643, 4465, 2, 45, 6));

Javascript Time Complexity Analysis

Hi there I have been researching and trying to learn how to check for the time complexity of certain algorithms. I've seen this video which was very helpful.
That being said I wondered off and started trying to work out the Worsts Case and an average case of certain algorithms.
1
I believe in the following snippet it is O(n) since to ind the value for sin we have to loop the entire array.
function mySin(x, iterNum) {
var mxx = -x*x;
var sin = 1;
var n = 0;
var term = 1;
for (var i = 1; i <= 2*iterNum; i++) {
n = n + 2;
term = term * mxx / ( n*(n+1) );
sin = sin + term
}
sin = x*sin;
console.log(sin + " = my function.");
console.log(Math.sin(x) + " math.sin");
}
Thanks again
2
function calculateFibonacciSum (num) {
if(cachedNumbers[num]) {
return cachedNumbers[num];
}
if(('number' === typeof num) && num <= 0) {
throw new Error ('Fibonnci series starts with 0. Please, enter any interget greater than or equal to 0');
}
else if(('number' === typeof num) && num === 0) {
return 0;
}
else if(('number' === typeof num) && (num === 1 || num === 2)) {
return 1;
}
else {
var value = calculateFibonacciSum(num-1) + calculateFibonacciSum(num-2);
cachedNumbers[num] = value;
return value;
}
}
While for this one I think it is also O(n) since in the first if/else statement the tc is O(1) since its contestant whilst the final else statement we must loop all the numbers and if the number is not calculated then call the function again (aka recurssion).
TIA
Both of these seem correct to me. Here's a bit more explanation:
1.
This is in fact O(n), as there are n iterations of the loop, the rest constant time; and n is proportional to iterNum
2.
This one is also linear time, but only since you cache the results of previous calculations. Otherwise it would be O(2n).
It is linear time since it essentially runs a loop down to the base cases (0 and 1). In fact, you could re-write this one using a loop instead of recursion.

Determine number of leading zeros in a floating point number

How can I calculate how many zeros come after the decimal point but before the first non-zero in a floating point number. Examples:
0 -> 0
1 -> 0
1.0 -> 0
1.1 -> 0
1.01 -> 1
1.00003456 ->4
Intuitively I assume there is a math function that provides this, or at least does the main part. But I can neither recall nor figure out which one.
I know it can be done by first converting the number to a string, as long as the number isn't in scientific notation, but I want a pure math solution.
In my case I don't need something that works for negative numbers if that's a complication.
I'd like to know what the general ways to do it are, irrespective of language.
But if there is a pretty standard math function for this, I would also like to know if JavaScript has this function.
As a sidenote, I wonder if this calculation is related to the method for determining how many digits are required for the decimal representation of an integer.
Let x be a non-whole number that can be written as n digits of the whole part, then the decimal point, then m zeroes, then the rest of the fractional part.
x = [a1a2...an] . [0102...0m][b1b2...bm]
This means that the fractional part of x is larger than or equal to 10–m, and smaller than 10–m+1.
In other words, the decimal logarithm of the fractional part of x is larger than or equal to –m, and smaller than –m+1.
Which, in turn, means that the whole part of the decimal logarithm of the fractional part of x equals –m.
function numZeroesAfterPoint(x) {
if (x % 1 == 0) {
return 0;
} else {
return -1 - Math.floor(Math.log10(x % 1));
}
}
console.log(numZeroesAfterPoint(0));
console.log(numZeroesAfterPoint(1));
console.log(numZeroesAfterPoint(1.0));
console.log(numZeroesAfterPoint(1.1));
console.log(numZeroesAfterPoint(1.01));
console.log(numZeroesAfterPoint(1.00003456));
As a sidenote, I wonder if this calculation is related to the method for determining how many digits are required for the decimal representation of an integer.
In the same manner, a positive integer x takes n decimal digits to represent it if and only if n - 1 <= log10(x) < n.
So the number of digits in the decimal representation of x is floor(log10(x)) + 1.
That said, I wouldn't recommend using this method of determining the number of digits in practice. log10 is not guaranteed to give the exact value of the logarithm (not even as exact as IEEE 754 permits), which may lead to incorrect results in some edge cases.
You can do it with a simple while loop:
function CountZeros(Num) {
var Dec = Num % 1;
var Counter = -1;
while ((Dec < 1) && (Dec > 0)) {
Dec = Dec * 10;
Counter++;
}
Counter = Math.max(0, Counter); // In case there were no numbers at all after the decimal point.
console.log("There is: " + Counter + " zeros");
}
Then just pass the number you want to check into the function:
CountZeros(1.0034);
My approach is using a while() loop that compares the .floor(n) value with the n.toFixed(x) value of it while incrementing x until the two are not equal:
console.log(getZeros(0)); //0
console.log(getZeros(1)); //0
console.log(getZeros(1.0)); //0
console.log(getZeros(1.1)); //0
console.log(getZeros(1.01)); //1
console.log(getZeros(1.00003456)); //4
function getZeros(num) {
var x = 0;
if(num % 1 === 0) return x;
while(Math.floor(num)==num.toFixed(x)) {x++;}
return(x-1);
}
You can do it with toFixed() method, but there is only one flaw in my code, you need to specify the length of the numbers that comes after the point . It is because of the way the method is used.
NOTE:
The max length for toFixed() method is 20, so don't enter more than 20 numbers after . as said in the docs
var num = 12.0003400;
var lengthAfterThePoint = 7;
var l = num.toFixed(lengthAfterThePoint);
var pointFound = false;
var totalZeros = 0;
for(var i = 0; i < l.length; i++){
if(pointFound == false){
if(l[i] == '.'){
pointFound = true;
}
}else{
if(l[i] != 0){
break;
}else{
totalZeros++;
}
}
}
console.log(totalZeros);
Extra Answer
This is my extra answer, in this function, the program counts all the zeros until the last non-zero. So it ignores all the zeros at the end.
var num = 12.034000005608000;
var lengthAfterThePoint = 15;
var l = num.toFixed(lengthAfterThePoint);
var pointFound = false;
var theArr = [];
for(var i = 0; i < l.length; i++){
if(pointFound == false){
if(l[i] == '.'){
pointFound = true;
}
}else{
theArr.push(l[i]);
}
}
var firstNumFound = false;
var totalZeros = 0;
for(var j = 0; j < theArr.length; j++){
if(firstNumFound == false){
if(theArr[j] != 0){
firstNumFound = true;
totalZeros = totalZeros + j;
}
}else{
if(theArr[j] == 0){
totalZeros++;
}
}
}
var totalZerosLeft = 0;
for (var k = theArr.length; k > 0; k--) {
if(theArr[k -1] == 0){
totalZerosLeft++;
}else{
break;
}
}
console.log(totalZeros - totalZerosLeft);

Algorithm that involves rounding and multiples

So I have a problem where I have an array of some length (usually long). I have an initial start index into that array and a skip value. So, if I have this:
var initial = 5;
var skip = 10;
Then I'd iterate over my array with indexes 5, 15, 25, 35, etc.
But then I may get a new start value and I need to find the closest value to the initial plus or minus a multiple of the skip and then start my skip. So if my new value is 23 then I'd iterate 25, 35, 45, etc.
The algorithm I have for this is:
index = (round((start - initial) / skip) * skip) + initial
And then I need a check to see if index has dropped below zero:
while(index < 0) index += skip;
So my first question is if there's a name for this? A multiple with random start?
My second question is if there's a better way? I don't think what I have is terribly complicated but if I'm missing something I'd like to know about it.
If it matters I'm using javascript.
Thanks!
Edit
Instead of
while(index < 0) index += skip;
if we assume that both initial and skip are positive you can use:
if (index < 0) index = initial % skip;
To get the closest multiple of a number to a test number: See if the modulo of your test number is greater than number/2 and if so, return number - modulo:
function closestMultiple(multipleTest,number)
{
var modulo = multipleTest%number;
if(0 == modulo )
{
return multipleTest;
}
else
{
var halfNumber = number/2;
if(modulo >= halfNumber)
{
return multipleTest + (number-modulo);
}
else
{
return multipleTest - modulo;
}
}
}
To check if a number is a multiple of another then compare their modulo to 0:
function isMultiple(multipleTest,number)
{
return 0 == multipleTest%number;
}
You might want to add some validations for 0 in case you expect any inside closestMultiple.
The value of index computed as you put it
index = round((start - initial)/skip) * skip + initial
is indeed the one that minimizes the distance between the sequence with general term
aj = j * skip + initial
and start.
Therefore, index can only be negative if start lies to the left of
(a-1 + a0)/2 = initial - skip/2
in other words, if
start < initial - skip/2.
So, only in that case you have to redefine index to 0. In pseudo code:
IF (start < (initial - skip/2))
index = 0
ELSE
index = round((start - initial)/skip) * skip + initial
Alternatively, you could do
index = round((start - initial)/skip) * skip + initial
IF index < 0 THEN index = 0
which is the same.
No while loop required:
function newNum(newstart, initial, skip) {
var xLow = newstart + Math.abs(newstart - initial) % skip;
var xHi = newstart + skip;
var result = (xLow + xHi) / 2 > newstart ? xLow : xHi;
if (result < 0) result += skip;
return result;
}
Take the distance between your new starting point and your initial value, and find out what the remainder would be if you marched towards that initial value (Modulus gives us that). Then you just need to find out if the closest spot is before or after the starting point (I did this be comparing the midpoint of the low and high values to the starting point).
Test:
newNum(1, 20, 7) = 6
newNum(-1, 20, 7) = 6
newNum(180, 10, 3) = 182
(Even though you stated in your comments that the range of the new starting point is within the array bounds, notice that it doesn't really matter).

Need help making an approximation of Euler's constant

It's very close but just one number off. If you can change anything here to make it better it'd be appreciated. I'm comparing my number with Math.E to see if I'm close.
var e = (function() {
var factorial = function(n) {
var a = 1;
for (var i = 1; i <= n; i++) {
a = a * i;
}
return a;
};
for (var k = 0, b = []; k < 18; k++) {
b.push(b.length ? b[k - 1] + 1 / factorial(k) : 1 / factorial(k));
}
return b[b.length - 1];
})();
document.write(e);document.write('<br />'+ Math.E);​
My number: 2.7182818284590455
Math.E: 2.718281828459045
Work from higher numbers to lower numbers to minimize cancellation:
var e = 1;
for(var k = 17; k > 0; --k) {
e = 1 + e/k;
}
return e;
Evaluating the Taylor polynomial by Horner's rule even avoids the factorial and allows you to use more terms (won't make a difference beyond 17, though).
As far as I can see your number is the same as Math.E and even has a better precision.
2.7182818284590455
2.718281828459045
What is the problem after all?
With javascript, you cannot calculate e this way due to the level of precision of javascript computations. See http://www.javascripter.net/faq/accuracy.htm for more info.
To demonstrate this problem please take a look at the following fiddle which calculates e with n starting at 50000000, incrementing n by 1 every 10 milliseconds:
http://jsfiddle.net/q8xRs/1/
I like using integer values to approximate real ones.
Possible approximations of e in order of increasing accuracy are:
11/4
87/32
23225/8544
3442297523731/1266350489376
That last one is fairly accurate, equating to:
2.7182818284590452213260834432
which doesn't diverge from wikipedia's value till the 18th:
2.71828182845904523536028747135266249775724709369995
So there's that, if you're interested.

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